Stable Pattern in the Mercuric Iodide Crystal

However, a region is found of initial inner iodide concentration, where a stationary pattern of alternating metastable/stable crystals is formed. A th...
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Alternating Metastable/Stable Pattern in the Mercuric Iodide Crystal Formation Outside the Ostwald Rule of Stages Mahmoud M. Ayass,† Andrew Abi Mansour,‡ and Mazen Al-Ghoul*,† †

Department of Chemistry, American University of Beirut, P.O. Box 11-0236, Beirut 1107 2020, Lebanon Department of Chemistry, Indiana University, 800 East Kirkwood Avenue, Bloomington, Indiana, United States

‡

ABSTRACT: We report a reaction−diffusion system in which two initially separated electrolytes, mercuric chloride (outer) and potassium iodide (inner), interact in a solid hydrogel media to produce a propagating front of mercuric iodide precipitate. The precipitation process is accompanied by a polymorphic transformation of the kinetically favored (unstable) orange, (metastable) yellow, and (thermodynamically stable) red polymorphs of HgI2. The sequence of crystal transformation is confirmed to agree with the Ostwald Rule of Stages. However, a region is found of initial inner iodide concentration, where a stationary pattern of alternating metastable/stable crystals is formed. A theoretical model based on reaction diffusion coupled to a special nucleation and growth mechanism is proposed. Its numerical solution is shown to reproduce the experimental results.

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yellow, and red in color.10 The orange phase is a kinetically favored yet thermodynamically unstable form of HgI2. Under ambient conditions, it comprises three different structures built of corner-shared Hg4I10 supertetrahedra.11,12 The second polymorph is also thermodynamically unstable: the yellow orthorhombic (β-HgI2) polymorph that possesses a molecular structure of nearly linear (178.3°) I−Hg−I molecules stacked in a layered fashion.13−15 We refer to it as metastable yellow or yellowM. Appearing last and most thermodynamically stable form of all is the red form (α-HgI2). It exhibits a tetragonal structure that comprises layers of corner-linked HgI4 tetrahedra, stacked by I···I contacts.10,14,15 In this study, we report a system of precipitating mercuric iodide from its precursor salts, mercuric chloride and potassium iodide. The precipitate is produced in a gel media, which forces gradual crystal growth and allows for detailed inspection of every stage of polymorphic transformation. Upon alteration of initial reaction concentrations, a region is found to attribute a rather puzzling phenomenon, where the crystal growth proceeds in an alternating manner in which both the stable and metastable forms of HgI2 coexist.

INTRODUCTION The kinetic pathway of the phase transformation during crystallization from amorphous phases and melts critically influence shapes and sizes of crystals, thus expressing their final physical properties.1 “When leaving a given state and in transforming to another state, the state that is sought out is not the thermodynamically stable one but the state nearest in stability to the original state.” This comes to be the most significant sentence stated by Wilhelm Ostwald in his remarkable paper entitled “Studien ueber die Bildung und Umwandlung fester Koerper” (“Studies of the Formation and Transformation of Solid Substances”).2 This sentence has subsequently become commonly known in English as Ostwald’s Rule of Stages. Simply speaking, if a compound is capable of crystallizing in different forms, the first structure it acquires, by spontaneous crystallization, would be the least stable one, which is followed successively by forms of increasing stability until the final and most thermodynamically stable form is attained. This gives proof to existence of intermediate metastable states forming in the process of crystal growth. Therefore, the understanding of these intermediate states would postulate new intuition about kinetics of transformation during crystallization and be the initial important step toward control of overall crystallization behavior.3 In this work, we are interested in the crystal formation of mercury(II) iodide (HgI2). Owing to its important optoelectronic properties4 and vast applications in high-energy resolution X-ray and gamma ray spectrometers,5 many studies have been conducted on HgI2 crystals whether recrystallized from organic solvents6 or grown in hydrogel media.7−9 Among the mercury(II) halides, HgI2 embraces the largest number of fascinating solid phases that adopt remarkable crystal structures. It is known to crystallize into three polymorphs that are orange, © XXXX American Chemical Society

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EXPERIMENTAL SECTION The materials we use in our experiments include: mercuric chloride (Fischer Chemical), potassium iodide (Merck), and agar gel (Bacto). We carry out all experiments in gel media. We use double distilled water to prepare stock solutions of both mercuric chloride (HgCl2) and potassium iodide (KI) according to the required concentrations. In a specific volume Received: June 11, 2014 Revised: July 31, 2014

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behind it in the mid region of the precipitation band, where the earlier formed yellowM crystals exist. There also exists an interesting reaction happening at the interface as a result of excess outer ions resulting with a redissolution of the precipitate to produce the complex K2HgI4. This complex is colorless and occupies the space between the interface and the precipitation band. This sequence of diffusion and polymorphic transformation is the typical behavior we encounter in all of our experiments, but while investigating all alterations of initial concentrations (i.e., inner concentration, outer concentration, and gel percentage), we discover a region that denies this progression. The inner electrolyte, [I−]0, reveals a significant impact on the behavior of the precipitate formation and polymorphic transformation. To test this effect, we prepare a range of different inner concentration at constant outer concentration and constant gel percentage. We use outer ([Hg2+]0 = 0.25 M) and inner ([I−]0 = (0.005, 0.05, 0.10, 0.15) M) in 1% agar gel. After a period of time (∼1 week) of diffusion, we take a snapshot of the tubes appearing in Figure 1. The highest inner

of KI solution, we dissolve agar powder (1% volume) by using a magnetic stirring rod on a stirring/hot plate. We maintain the temperature of the mixture at a range within 80−90 °C. To ensure that no errors in the concentration occur we make sure that the solutions never reach the boiling point. The solutions continue to mix until they become very clear, and no gel particles remain floating, thus completing the inner electrolyte mixture preparation. Next, using a Pasteur pipet, we transfer the gel mixture, while hot, into a thin tube having dimensions of 6 mm diameter and 20 cm length. About 2 mL of the solution is transferred, which fills up about two-thirds of the tube. We then cover the opening of the tubes with paraffin film and place them in a chamber equipped with a thermostat that maintains the temperature at 24.0 ± 0.2 °C. The gels are left for 2 h for their gelation and aging processes to complete. Next, a simple HgCl2 solution serves as the outer electrolyte used in our experiment. Therefore, we proceed with the performance of the reaction by delivering the HgCl2 solutions into the tubes over the solidified gel also by the means of a Pasteur pipet (initialization step). The tubes are left for days for reaction and diffusion to proceed sufficiently. The HgI2 precipitate produces interesting crystals and patterns, which we monitor under a high-resolution digital camera (Cannon EOS 450D) connected to an iMac with a built-in remote shooting software, where the camera options can be altered according to needed specifications.

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RESULTS AND DISCUSSION Under ambient conditions, the unstable orange and yellow phases cannot be easily isolated, thus upon the slightest touch they promptly transform into the thermodynamically stable red phase, each in its own manner. However, the orange phase is noticeably more stable than the yellowM phase under ambient conditions. The orange-to-red transformation occurs within hours by a process involving the formation of irregularly shaped red nuclei that spread along the whole structure while maintaining the shape of the crystal. A red front is formed in the yellowM crystals, at the point of contact, that transmits quickly to transform the whole crystal within seconds, notably distorting its structure. Seemingly, only the movement of Hg atoms in an invariant ccp matrix of I atoms is involved in the transformation from orange to red. In contrast, a complete rearrangement of the atoms occurs in the transformation from yellow to red.10,16 When the prepared gel mixtures solidify, we begin our reactions by delivering the outer electrolyte, [Hg2+]0, into the tubes, thus initiating the reaction−diffusion process. Instantly, when the two initially separated electrolytes meet (gel interface), a precipitation zone of kinetically favored orange HgI2 forms and diffuses along the tube, forming a band of microscopically structured crystals that gradually convert to the yellowM form of HgI2. As the diffusion continues, the yellowM polymorph dominates most of the precipitation band and exhibits a more significant crystal structure than the orange polymorph, in which it takes the shape of threads having branching structures along their lengths. As the precipitation band grows with time, a fascinating polymorphic transformation takes place, converting the yellowM polymorph into the final and thermodynamically favored form of HgI2, the red polymorph. The red crystals always adopt a needle-like structure, appearing from within the yellowM crystals. The leading band is always composed of the kinetically favored yellowM crystals, and the polymorphic transformation occurs

Figure 1. Snapshot of four tubes with different initial inner iodide concentrations expressing the features of the three concomitant HgI2 polymorphs (orange-yellow-red). The tubes display the transition from the regular polymorphic transformation progression to the alternating regime. The black line at the edge of the tubes indicates the outer/inner electrolytes intersection (gel interface). Initial conditions: inner iodide concentration, [I−]0 = (A) 0.15, (B) 0.10, (C) 0.05, (D) 0.005 M, all in 1% by volume agar gel; at constant outer mercuric concentration, [Hg2+]0 = 0.25 M. Scale bar represents 1.0 cm.

concentrations (Figure 1A,B) exhibit the typical behavior of precipitation explained previously, yet as the concentration decreases (Figure 1C), we notice a change in the form of the color and alignment of the precipitation band. The behavior enhances and actually unveils in Figure 1D in the lowest concentration of the inner electrolyte. A fascinating, unusual coexistence of the metastable (yellow) polymorph and the stable (red) polymorph appears. These bands form in a manner similar to what is perceived in the famous Liesegang bands,17−22 yet the deviation in this type of banding is that the precipitate is continuous and no voids of none or minimal B

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The effect of the gel matrix also plays an important role in the exhibited pattern. If the experiment is carried in gelatin matrix, for example, no alternation is detected. It is obvious that the gel structure, its pore size, and distribution as well as its chemical nature interact with the polymorphs and their transformation. In 1897, Ostwald empirically stated in his step rule of stages that a system in an unstable state does not necessarily transform directly into the most thermodynamically stable state, thus implying the existence of metastable intermediate states.2 This rule undoubtedly applies to our system and several other previously reported systems similar to ours. Such systems involve the polymorphic transformation of nickel and cobalt hydroxide precipitates,17,23−25 yet in the mercuric iodide system the alternating pattern between the metastable and stable forms of the crystals is exceptional. In this region of concentration ([I−]0 = 0.003 to 0.006 M), a transition occurs in which the crystal transformation stops abiding by the Ostwald rule of stages and enters a regime that favors oscillatory crystal formation. This anomalous behavior might be due to a bifurcation leading to a physical instability where the interplay of reaction−diffusion with nucleation, growth, and competitive particle sizes plays a major role.

nucleation is present. In comparison with the Liesegang bands, the yellow regions act like the voids and the red regions take the part of the nucleating bands. In addition, the redissolution reaction, occurring from the interface, is most significant in the tubes with higher concentration gradients between the inner and outer electrolytes. To specifically confirm this phenomenon, we prepare a set of inner concentrations around this concentration (0.005 M), and we find that this behavior reproduces in the range between 0.003 and 0.006 M of inner [I−]0. We reproduce the tube with the experimental parameters of inner ([I−]0 = 0.005 M in 1% agar gel) and outer ([Hg2+]0 = 0.25 M) several times and monitor its diffusion hourly. We then take a snapshot every 24 h to compile a panel (Figure 2) representing the evolution of

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THEORY AND SIMULATION The Model. The Liesegang phenomenon is typically modeled using reaction−diffusion equations coupled to nucleation and growth equations.26−29 Such models depend on parameters critical to the nucleation and growth phenomena. Because precipitation inherently involves Ostwald’s ripening, the Lifshitz−Slyozov instability30 leads to a constraint on these critical parameters. In this section, we introduce a reaction−diffusion model that describes the dynamics of the mercuric iodide system when the transition to alternating bands takes place, that is, in the range [I−]0 = 0.003 to 0.006 M. We show that in order to reproduce alternating Liesegang bands, the constraint imposed by the Lifshitz−Slyozov instability must be replaced with another that extends the nucleation stage over that of polymorphic transition. This increases the stability of the α-HgI2 polymorph in such a way that its spatiotemporal distribution alternates with that of the β-HgI2 polymorph. The model is based on two reaction−diffusion equations that describe the principal reaction A + 2B → C between mercury II, denoted (A), and iodide, denoted (B), and their diffusion in the liquid phase:

Figure 2. Panel of compiled snapshots of the daily evolution of the alternating yellow (metastable)/red (stable) pattern of the HgI2 crystals. The black line at the edge of the tubes indicates the outer/ inner electrolytes intersection (gel interface). Initial conditions: inner iodide concentration, [I−]0 = 0.005 M in 1% by volume agar gel; at constant outer mercuric concentration, [Hg2+]0 = 0.25 M. Scale bar represents 1.0 cm.

the precipitation band over a period of 9 days. From Figure 2, it is clear that in the early stages of diffusion the orange polymorph is dominant and transforms to the yellowM polymorph. As diffusion continues, the metastable yellow polymorph does not transform to the stable red polymorph as expected. Through the analysis of many snapshots taken of the evolution, we predict that each of the polymorphs forms separately. The yellow appears first and extends in space to form a band until its production halts when the red band appears thereafter. This repetitive formation of the yellow and red bands eventually gives rise to the observed alternating pattern of metastable/stable mercuric iodide. It is also obvious from Figure 2 that each produced band is perfectly stationary and does not diffuse through the length of the tube. What is also interesting, as seen in the late stages of the evolution, is that the “older” yellowM bands that appear do not transform to the stable red polymorph but actually dissolve upon the redissolution reaction taking place owing to the excess outer ions. This fact clearly appears in the last 3 days in Figure 2 because the previously yellow parts have become nearly colorless and the crystals in those regions are not entirely red. It is also worth noticing that the redissolution region is proportional to the time elapsed of the reaction.

∂A = −∇·JA − R ∂t

(1)

∂B = −∇·JB − 2R ∂t

(2)

where R is the rate of the chemical reaction, and it takes the mean-field expression R = kAB2, and k is the rate constant. Diffusion is described in terms of the flux J, which is assumed to follow Fick’s second law, that is, JX = −ΓX∇X for chemical species X of concentration (X). The intermediate (C) that is formed represents HgI2 in the colloid form, and it undergoes both diffusion and nucleation in the absence of convection: ∂C = −∇·JC + R − vn − vg ∂t C

(3)

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Figure 3. (A) Normalized spatial distributions of stable α-HgI2 (red curve) and metastable β-HgI2 (orange curve) polymorphs at t = 106 using the parameters shown in Table 1. The initial concentrations are taken to be a0 = 100 and b0 = 5. (B) Color map (projection of the 1D simulation in panel A into a rectangular grid) of the densities of α-HgI2 (red curve) and β-HgI2 (orange curve) polymorphs at t = 106 exhibiting alternating pattern of the two polymorphs using the same parameters as those in panel A except k = 10−7 and Γc = 0.04. For better visualisation, the concentration of the β polymorph was raised to the power 0.25 and that of the α polymorph to the power 1.5.

where vn is the rate of nucleation and vg is that of growth. Many phenomenological models based on treating nucleation and growth as piece-wise continuous processes in space and time have been proposed, and they are shown to reproduce the Liesegang pattern on both simple31 and complicated geometries.32 In such methods, the precipitate is taken to be a distribution of a discrete set of particles of various sizes. For the system under study, we will assume that HgI2 precipitates into two distinct forms: (i) stable polymorph denoted (α) or (ii) metastable polymorph denoted (β). Diffusion in the solid phase is assumed to be negligible. Because the form of the nucleation and growth rate functions do not alter the final pattern observed,26 the following linear forms are respectively chosen vn = k n(C − cn)H(C − cn)

(4)

vg = kg(C − cg)H(C − cg)α

(5)

vt = k t(C − ct)H(C − ct)β

In classical Liesegang systems, the β particles could dissolve back to replenish (C). Here this process either is considered to be kinetically hindered or the β particles must have an additional thermodynamic stability. Therefore, dissolution of the β particles is not included in the model. This is based on the experimental observation that the β polymorph has a sustaining stability. Furthermore, it was previously reported28 that for classical Liesegang systems the Lifshitz−Slyozov instability leads to a constraint on the critical parameters: cn > ct > cg. If we define cmax = maxx,y(C), then this temporal function should approximately oscillate between cg and cn.32 In this case, polymorphic transition takes place whenever the β particles are being formed, that is, when cmax ≥ cn, and it persists when cmax ∈ [ct,cn). This does not lead to alternating phases but rather discontinuous Liesegang band formation in the α particles. Because the mercuric iodide system does not obey the Ostwald rule of stages, it is not surprising that this condition is not satisfied here. Instead, priority is given to nucleation over polymorphic transition, which leads to the constraint

H is the Heaviside unit-step function and kn and kg are the rate constants for the nucleation and growth mechanisms, respectively. The critical constants cn and cg are characteristic parameters of the system under study, and they play an important role in the final pattern observed. The dynamical equations describing the solid phase take the form

∂β = vn − vt ∂t

(6)

∂α = vt + vg ∂t

(7)

(8)

ct > cn > cg

(9)

In this case, nucleation takes place when cmax ∈ [cn,ct], whereas polymorphic transition occurs only when cmax ≥ ct. Thus, the spatial distribution of the β polymorph extends that of the α polymorph. As a consequence, for an alternating phase distribution, the polymorphic transition rate vt must be much faster than all other processes taking place. If this condition is not met, alternating bands are lost and in this case a

The rate of transition takes a linear form in terms of C and the critical parameter of nucleation ct as follows D

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propagating band of β particles is observed, while the α polymorph forms Liesegang bands. (See Figure 7.) The model introduced can be therefore summarized as follows: (1) The precipitate exists in two discrete states: (i) β polymorph (metastable state) or (ii) α polymorph (stable state). (2) The β particles encountered in this system are more stable than those formed in classical Liesegang systems. This is because either the nuclei are larger in size (they are more thermodynamically stable) or their dissolution is a kinetically hindered process. (3) The constraint required for Lifshitz−Slyozov instability is violated as a consequence of the metastable state of the β particles. (4) The transition rate from β to α particles must be much faster than all other processes so that the spatial distribution of the β polymorph alternates with that of the α polymorph. The suggested model and the derived condition are validated in the next subsection by numerically solving eqs 1−3, 6, and 7. Simulation. The complete reaction−diffusion model can be written as a set of coupled partial differential equations ∂A = ∇·ΓA∇A − kAB2 ∂t

(10)

∂B = ∇·ΓB∇B − 2kAB2 ∂t

(11)

Figure 4. Spatial distributions of β-HgI2 polymorphs at t = 106 using the rate constants shown in Table 1, initial concentrations a0 = 100 and b0 = 5, and constants cg = 0.1, cn = 0.3, ct = 0.2 (line) and cn = 0.2, ct = 0.3 (dashed line). In the first case (cn > ct), the critical nucleation and growth constants obey the Lifshitz−Slyozov instability; that is, they violate eq 9. The β polymorph is therefore unstable and completely vanishes.

∂C = ∇·ΓC∇C + kAB2 − k n(C − cn)H(C − cn) ∂t − kg(C − cg)H(C − cg)α

(12)

∂β = k n(C − cn)H(C − cn) − k t(C − ct)H(C − ct)β ∂t (13)

∂α = k t(C − ct)H(C − c t)β + kg(C − cg)H(C − cg)α ∂t (14) 33

Using the method of lines, these equations are solved on a 1D grid of uniform spacing set to 0.1 and on a total number of 2 × 104 grid points. Initially (at t = 0), the components (A) and (B) are separated in space such that the first occupies the left half of the system with a homogeneous concentration a0 and is zero everywhere else, while the second component (B) has a homogeneous concentration b0 on the right half of the system and is zero everywhere else. All other components(C), (α), and (β)are zero everywhere. On the boundaries, zero-flux conditions are imposed on all chemical species. Equations 10−14 are discretized in space using the central finite difference method (since diffusion is isotropic). A variable order (up to fourth) and adaptive step-size implicit time integrator based on backward differentiation formulas34 was used to integrate the resulting stiff ordinary differential equations in time. The reaction rate constant k was taken to be 10−5, and the diffusion coefficients were all set to 0.1. The nucleation and growth rate constants and critical parameters that satisfy eq 9 used in producing the results shown in Figures 3, 5, and 6) are given in Table 1. In Figure 4, the classical Liesegang pattern is obtained by setting the critical nucleation and growth constants to follow the Lifshitz−Slyozov instability; that is, eq 9 is violated. The β polymorph in this case is unstable; the alternating pattern is

Figure 5. Spatial distributions of stable α-HgI2 (red curve) and metastable β-HgI2 (orange curve) polymorphs at t = 106 using the parameters shown in Table 1. The initial concentration of the inner electrolyte is taken to be b0 = 2.5, and that of the outer electrolyte is a0 = 100.

lost, and instead the classical Liesegang pattern is recovered in the form of α polymorph bands. The concentration of the inner electrolyte b0 is decreased from 5 to 2.5 (Figure 5) and then increased from 5 to 10 (Figure 6) to investigate the dependence of the alternating pattern on the initial state of the system. In both simulations, the alternating pattern persists as b0 is varied. Finally, the impact of the rate of transition vt on the alternating pattern is investigated. In the previous section, we conjectured that this rate must be much larger than that of nucleation. Thus, kt was set to 1 and kn was set to 10−4 (see Table 1) in all simulations shown in Figures 3−6. In Figure 7, we show that when kt is close in range to kn (keeping all other parameters in Table 1 constant), the alternating pattern is lost. E

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most thermodynamically stable red polymorph via the metastable yellow polymorph. This sequence is confirmed to be in agreement with the Ostwald rule of stages, yet we discover a region of inner mercuric concentration in which a pattern of alternating metastable and stable crystals unveils. The preference of crystal growth is oscillatory in this region, thus producing a stationary pattern of yellow and red HgI2 crystals. A model that incorporates reaction−diffusion, nucleation, and growth is suggested and shown to reproduce this polymorphic alternation pattern.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +961-1-350000, ext. 3999. Fax: +961-1-365217. Email: [email protected]. Notes

The authors declare no competing financial interest.

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Figure 6. Normalized spatial distributions of stable α-HgI2 (red curve) and metastable β-HgI2 (orange curve) polymorphs at t = 106 using the parameters shown in Table 1. The initial concentration of the inner electrolyte is taken to be b0 = 10, and that of the outer electrolyte is a0 = 100.

ACKNOWLEDGMENTS This work is supported by the Lebanese Council for National Scientific Research (LCNSR) and the University Research Board, American University of Beirut.

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Table 1. Nucleation and Growth Parameters Used in Simulating Alternating Bands in Figures 3, 5, and 6 cg

cn

ct

kn

kt

kg

0.1

0.2

0.3

10−4

1.0

10−2

REFERENCES

(1) Burda, C.; Chen, X.; Narayanan, R.; El-Sayed, M. A. Chemistry and Properties of Nanocrystals of Different Shapes. Chem. Rev. 2005, 105, 1025−1102. (2) Ostwald, W. Studies on the Formation and Inversion of Solids. First Paper: Supersaturation and Supercooling. Z. Phys. Chem., Stoechiom. Verwandtschaftsl. 1897, 22, 289. (3) Chung, S.-Y.; Kim, Y.-M.; Kim, J.-G.; Kim, Y.-J. Multiphase Transformation and Ostwald’s Rule of Stages During Crystallization of a Metal Phosphate. Nat. Phys. 2008, 5, 68−73. (4) Bube, R. H. Opto-Electronic Properties of Mercuric Iodide. Phys. Rev. 1957, 106, 703−717. (5) Schieber, M.; Roth, M.; Schnepple, W. F. Crystal Growth and Applications of Mercuric Iodide. J. Cryst. Grow. 1983, 65, 353−364. (6) Piechotka, M. Mercuric Iodide for Room Temperature Radiation Detectors. Synthesis, Purification, Crystal Growth and Defect Formation. Mater. Sci. Eng., R 1997, 18, 1−98. (7) Das, I.; Pushkarna, A.; Agrawal, N. R. Chemical Waves and LightInduced Spatial Bifurcation in the Mercuric Chloride-Potassium Iodide System in Gel Media. J. Phys. Chem. 1989, 93, 7269−7275. (8) Das, I.; Pushkarna, A.; Bhattacharjee, A. New Results on LightInduced Spatial Bifurcation and Electrical Field Effect on Chemical Waves in the Mercury (II) Chloride-Potassium Iodide System in Gel Media. J. Phys. Chem. 1990, 94, 8968−8973. (9) Das, I.; Pushkarna, A.; Bhattacharjee, A. Dynamic Instability and Light-Induced Spatial Bifurcation of Mercuric Iodide and External Electric Field Experiments in Two-Dimensional Gel Media. J. Phys. Chem. 1991, 95, 3866−3873. (10) Hostettler, M.; Birkedal, H.; Schwarzenbach, D. Polymorphs and Structures of Mercuric Iodide. Chimia 2001, 55, 541−545. (11) Hostettler, M.; Birkedal, H.; Schwarzenbach, D. The Structure of Orange HgI2. I. Polytypic Layer Structure. Acta Crystallogr., Sect. B: Struct. Sci. 2002, 58, 903−913. (12) Hostettler, M.; Schwarzenbach, D. The Structure of Orange HgI2. II. Diamond-Type Structure and Twinning. Acta Crystallogr., Sect. B: Struct. Sci. 2002, 58, 914−920. (13) Hostettler, M.; Birkedal, H.; Schwarzenbach, D. The Yellow Polymorphs of Mercuric Iodide (HgI2). Helv. Chim. Acta 2003, 86, 1410−1422. (14) Jeffrey, G. A.; Vlasse, M. Crystal Structures of the Red, Yellow, and Orange Forms of Mercuric Iodide. Inorg. Chem. 1967, 6, 396−399. (15) Paić, M.; Paić, V. Diffuse Reflectance Spectra and Polymorphism of Mercury (II) Iodide. Phys. Status Solidi A 1981, 68, 447−455.

Figure 7. Normalized spatial distributions of stable α-HgI2 (red curve) and metastable β-HgI2 (orange curve) polymorphs at t = 106 using the parameters shown in Table 1 except kt is taken to be equal to 10−5, and the initial concentrations are set to a0 = 100 and b0 = 5. The bands of β-HgI2 precipitate exhibit splitting each into two bands.

The β polymorph is still stable, but its distribution does not alternate with that of the alpha polymorph.

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CONCLUSIONS In summary, we report a mercuric iodide system precipitating in a solid hydrogel medium accompanied by a polymorphic transformation of its three concomitant polymorphs: the orange (unstable), yellow (metastable), and red (stable). The typical progression of crystal conversion is found to initiate with the unstable orange polymorph and terminate with the F

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The Journal of Physical Chemistry A

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dx.doi.org/10.1021/jp5058034 | J. Phys. Chem. A XXXX, XXX, XXX−XXX